For the quadratic equation 2x² - 4x - 48 = 0 value of x is 6 and -4.
What is quadratic equation?
The second-degree equation is a quadratic equation. This indicates that it has at least one (1) squared phrase. Ax2 + bx + c = 0 is one of the most used formulas for solving quadratic equations. Here, a, b, and c are constants or numerical coefficients. Here, the variable "X" is unknowable.
ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
We have a quadratic equation;
2x² - 4x - 48 = 0
To find the value of x we have to follow these steps ;
(2x^2 - 4x) - 48 = 0
Pull out like factors :
2x^2 - 4x - 48 = 2 • (x^2 - 2x - 24)
x2 multiplied by 2x and 24
x^2 is the initial term, and it has a coefficient of 1.
The coefficient of the middle term, which is -2x, is 2.
"The constant," the final term, is -24.
⇒ x^2 - 6x + 4x - 24
⇒ (x+4) • (x-6)
⇒ 2 • (x + 4) • (x - 6) = 0
therefore x+4 = 0
x = -4
and x-6 = 0
Add 6 to both sides of the equation :
x = 6
Hence, for the quadratic equation 2x² - 4x - 48 = 0 value of x is 6 and -4.
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parallelogram cdef with vertices c(-4, -4), d(-2, 0), e(6, 1), and f(4, -3) in the line y = 2
The coordinates of the image of the parallelogram are:
C = (-4, 8)
D = (-2, 4)
E = (6, 3)
F = (4, 7)
What is a reflection?There are two ways of reflection.
Along x-axis:
(x, y) – (x, -y)
Along y-axis:
(x, y) - (-x, y)
We have,
Parallelogram CDEF with vertices:
C = (-4, -4)
D = (-2, 0)
E = (6, 1)
F = (4, -3)
The parallelogram is reflected over the line y = 2.
This means,
The y-coordinates will change and the x-coordinate will remain the same.
Now,
C = (-4, -4)
There are 6 units between y = 2 and y = -4 so,
C' = (-4, 2 + 6) = (-4, 8)
D = (-2, 0)
There are 2 units between y = 2 and y = 0 so,
D' = (-2, 2 + 2) = (-2, 4)
E = (6, 1)
There are 1 units between y = 2 and y = 1 so,
E' = (6, 2 + 1) = (6, 3)
F = (4, -3)
There are 5 units between y = 2 and y = -3 so,
F' = (4, 2 + 5) = (4, 7)
Thus,
The coordinates of the image are:
C = (-4, 8)
D = (-2, 4)
E = (6, 3)
F = (4, 7)
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It costs $4 per ride at an amusement park, plus a $10 fee to get in. Write an equation to represent the total cost (y) for any number of rides (x).
An equation to represent the total cost (y) for any number of rides (x) is y = 4x + 10.
How to write an equation to represent the total cost (y)?In order to write an equation that model this situation, we would assign variables to the number of rides at an amusement park and the total cost respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of rides.Let the variable y represent the total cost.Next, we would translate the word problem into an algebraic equation based on the fact that it cost $4 per ride, plus a $10 fee to get in as follows;
y = 4x + 10.
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What is the area of a rectangle with a length of 14.4 inches and a width that is one-third of the length?
A .43.2 in.2
B .51.84 in.2
C .69.12 in.2
D .103.68 in.2
Answer:
C.
Step-by-step explanation:
The area of a rectangle is typically written as:
[tex]A = l x w[/tex]
where: l represents the length and w represents the width.
Since, in the given problem, we already know the value of the length which is 14.4 inches, and the value of width is one-third of the length. Thus, the width would be:
[tex]= (14.4)(\frac{1}{3})\\= \frac{24}{5} \\= 4.8 inches[/tex]
We will simply substitute this value to the formula to get the area.
[tex]A = lxw\\A = (14.4)(4.8)\\A = 69.12 in^{2}[/tex]
Answer:
its c i did this test
Step-by-step explanation:
2. Mai also got the expression 7x 1 and wrote her answer as 7x + (−1). Are the two
expressions equivalent? How do you know?
Answer:
Yes, the answers are equivalent.
Step-by-step explanation:
The answers are equivalent because when adding a positive to something it does not change the value of the number. So by adding the + in front of the -1 the value of -1 does not change in the equation.
Hope this helps!!
Can someone help me with this asap?!
Inequality of 4x-6= 22 is x=7
Explain about the Inequality?In mathematics, inequalities describe the connection between two values that are not equal. Equal implies to be equal, not. The "not equal symbol is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine if they are less than or higher than.
Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,,, or.
To the other side, move -6.
Changes from a -6 to a +6 sign.
4x-6+6= 22+6
4x= 22+6
4x= 28
Divide each side by 4
4x/4= 28/4
x= 7
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Two numbers are in the ratio 8cm:1m,if the smaller number is250,what is the greater number
Two numbers are in the ratio 8cm:1m, he greater number is 3,125.
What is ratio?A ratio in mathematics demonstrates how many times one number is present in another. A ratio can have any number of quantities, such as counts of people or things or measurements of length, weight, time, etc. Both numbers must be positive in most situations. An ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or the value represented by this fraction are all examples of ratios.
Given that, Two numbers are in the ratio 8cm:1m and smaller number is 250.
let the greater number is x.
ratio = 8cm/1m
= 8cm/100cm
= 1/12.5 or 1:12.5
1/12.5 = 250/x
⇒ x = 250 * 12.5
⇒ x = 3,125
So, the greater number is 3,125.
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there are 14 desktops and 16 laptops what percent of the computers are laptops
Answer:
53.3%
Step-by-step explanation:
14 + 16 = 30
16/30 x 100 = 53.3% are laptops
factor the common factor of 9x + 36
9 is the common factor of 9x + 36.
What is Number system?A number system is defined as a system of writing to express numbers.
The given expression is 9x+36
Factor is a number or algebraic expression that divides another number or expression evenly i.e., with no remainder.
The factors of 9 are 1,3,9
The factors of 36 are 1,2,3,4,6,9,12 and 18
The highest common factor is 9.
Take 9 as common from the expression.
9(x+4)
Hence, 9 is the common factor of 9x + 36.
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All 3 are really confusing me and I need help
If the denominator is having a poor integer, then we can multiply the numerator and denominator each through -1, to carry the minus signal at the top.
What is supposed through integer ?
The variety 0 (0), a tremendous natural variety (1, 2, three, and so on.), or a terrible integer denoted by way of a minus sign (1, 2, 3, and many others.) are all examples of integers.
The inverse components of the equal superb numbers are the bad numbers.
the lowest organization and ring of the natural numbers are fashioned by using the integers.
to distinguish them from the more common algebraic integers, the integers in algebraic quantity theory are every so often particular as rational integers.
In truth, (rational) integers are rational numbers which are also algebraic integers.
inside the beyond, the word was used to refer to a a couple of of 1 or the whole aspect of a blended quantity.
we will multiply and divide -five with the aid of (-1), to get;
(-five)*(-1) = five
as a result, five is a effective rational range.
1 can be expressed inside the form of ratio, such that,
1 = 1*1
wherein each numerator and denominator, i.e. 1 and 1 are high-quality integers.
therefore, 1 is a high quality rational wide variety.
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Exercise 2. 5. 2: Proof by contrapositive of statements about integer division. About Prove each statement by contrapositive (a) If x and y are integers such that 3xy then 3x. Solution (b) For any integers x, y, and z, if x|y and xz, then x(y z). (c) If x and y are integers such that x > 1, and x divides y, then x(y 1)
The statements
(a) If x and y are integers such that 3xy then 3x.
(b) For any integers x, y, and z, if x y and xz, then x(y - z).
(c) If x and y are integers such that x > 1 and if x divides y, then the solution is x(y - 1)
are proved.
The term integers in math is defined as are the collection of whole numbers and negative numbers.
Here we know that x and y are the integers,
Then it takes both positive and negative numbers.
Then we take y=1, then we apply it on the expression then we get,
=> 3x(1) = 3x.
Similarly here we have take that xy|z means xy is a factor of z,
Here we can say xym = z for some integer m.
=> x × ym = z, and ym is an integer by closure hence x is a factor of z such that x|z.
Similarly here we can also y * xm = z, and consider xm is an integer, hence y is a factor of z, i.e. y|z.
Where in the third one, we can take x|y means there exists a constant is written as y = kx
Where as y|x means there exists a constant written as x = cy
When we compare these, then we get,
=> y = kx = kcy
Here we have to true if kc = 1 and since k and c are integers, then we have k = c = 1
Therefore y = kx becomes y = 1*x or y = x
Similarly x = cy becomes x = 1*y or x = y
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can anyone help me with this?
$97.056 is the total interest accrued after the first month.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, You (or your parents) purchase a new car for $19,725.00 plus 4.75% sales tax. The down payment is $2,175.00 and you (or your parents) have an average credit rating.
The cost of car = 19,725*(1.0475) = 20,661.9375
Down payment = 2,175
So balance amount, P= 20661.9375-2175 = 18,486.9375
So interest for the average rating of a new car = 6.30%
So the interest accrued in first month = 18,486.9375*0.063/12 = $ 97.056
therefore, interest accrued after the first month is $97.056.
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a five-card hand is drawn from a standard 52-card deck all at once, so order doesn't matter. what is the probaility that the hand consists entirely of face crads (K, Q, and J are the ones called face cards)?
can i plese receive an explanation and help
Answer:
33/108290 = 0.000305
Step-by-step explanation:
There are 52 cards in a deck.
There are 3 face cards of each of 4 suits in a deck, so there are 12 face cards in a deck.
Taking all cards at once is the same as taking one card at a time with no replacement.
First card: p(face card) = 12/52 = 3/13
Now there are 11 face cards and a total of 51 cards left.
Second card: p(face card) = 11/51
Now there are 10 face cards and a total of 50 cards left.
Third card: p(face card) = 10/50 = 1/5
Now there are 9 face cards and a total of 49 cards left.
Fourth card: p(face card) = 9/49
Now there are 8 face cards and a total of 48 cards left.
Fifth card: p(face card) = 8/48 = 1/6
Since each drawing of a card is an independent event, the overall probability of drawing 5 face cards is the product of the individual probabilities.
p(5 face cards) = 3/13 × 11/51 × 1/5 × 9/49 × 1/6
p(5 face cards) = 33/108290 = 0.000305
The volume of soda dispensed in a can during production is normally distributed with a mean of 358. 2 ml and a standard deviation of 1. 8 ml. The company does not want more than 2. 5% of all cans to be less than the volume on the label which is 355ml. Is the company meeting its goal? If not, what should the company do? (Show work)
To meet the goal, the company should adjust the mean and/or standard deviation so that the probability of cans having a volume less than 355ml is less than 2.5%.
A probability is a numerical representation of the likelihood or chance that a specific event will take place.
We can use the z-score formula to find the probability of cans having a volume less than 355 ml.
z-score = (355 - 358.2) / 1.8 = -1.78
Probability of cans having a volume less than 355ml = P(z < -1.78) = 0.0372
The company is not meeting its goal since the probability of cans having a volume less than 355ml is 0.0372 which is greater than 2.5%.
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PLEASE HELP ASAP
The table represents a linear relationship.
x −2 0 2 4
y −1 0 1 2
Which of the following graphs shows this relationship?
A graph of a line passing through the points negative 2 comma negative 4 and 0 comma 0
B graph of a line passing through the points negative 2 comma negative 1 and 0 comma 0
C graph of a line passing through the points negative 2 comma 4 and 0 comma 0
D graph of a line passing through the points negative 2 comma 1 and 0 comma 0
A graph which shows this relationship is: B. graph of a line passing through the points negative 2 comma negative 1 and 0 comma 0.
How to determine the linear function?In order to determine the ordered pairs and linear function that could represent a linear relationship in the given table, we would have to determine the slope of based on the data points.
In Mathematics, the slope of a linear function can be calculated by using this this mathematical expression;
Slope = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope = (y₂ - y₁)/(x₂ - x₁)
Slope = (0 + 1)/(0 + 2)
Slope = 1/2
Slope = 0.5.
At data point (-2, -1), a linear function of this line can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represents the data points.y + 1 = 0.5(x + 2)
y = 0.5x + 1 - 1
y = 0.5x
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The average high temperatures in degrees for a city are listed. 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57 If a value of 42.5° is added to the data, how does the mean change and by how much? The means stays at 80.4°. The mean stays at 77.5°. The mean increases by 2.9°. The mean decreases by 2.9°.
The mean decreases by 2.9°. Therefore, option D is the correct answer.
What is the average?In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
Given that, the average high temperatures in degrees for a city are 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57.
Here, average = Sum of all the observations/Number of observations
= (58+61+71+77+91+100+105+102+95+82+66+57)/12
= 965/12
= 80.41°
New average = 965+42.5/12+1
= 1007.5/13
= 77.5°
Difference in average =80.41-77.5
= 2.91°
Therefore, option D is the correct answer.
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What is the value of P(X=3 or X=0)?
Enter your answer in the box.
P(X=3 or X=0) = __________
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Dr johnson is a clinical physiologist looking to test out a new therepy to help people that are scared of spiders he measured each person fear of spiders before the therapy and after the therapy in both colums of data he used the pulse rate of people when confronted by an actual spiders
Answer: Dr. Johnson is conducting an experimental study to test the effectiveness of a new therapy for individuals with arachnophobia, which is the fear of spiders. He is measuring the pulse rate of the participants before and after the therapy as an indicator of their fear response when confronted by an actual spider. The data collected will likely be used to determine if the therapy is effective in reducing the participants' fear of spiders as measured by their pulse rate.
It is important to note that while pulse rate is a good indicator of fear response, it is not the only indicator of fear and it is also not a definitive measure of the effectiveness of the therapy. Other factors such as self-reported fear, behavioral changes, and physiological changes should also be considered to get a comprehensive understanding of the therapy's effectiveness.
Step-by-step explanation:
Harper has $0.70 worth of nickels and dimes. She has 5 more nickels than dimes. By following the steps below, determine the number of nickels, x, and the number of dimes, y, that Harper has.? Determine three ways to have 5 more nickels than dimes
The number of nickels, x, and the number of dimes y that Harper has are;
8 nickels and 3 dimes
How to solve algebra word problems?From conversion of coins we know that;
1 nickel = $0.05
1 dime = $0.10
Thus, if she has 5 more nickels than dimes, then;
Let x = the number of dimes Harper has
Let x + 5 = the number of nickels Harper has
Thus;
$0.05(x + 5) + $0.10(x) = $0.70
0.05x + 0.25 + 0.10x = 0.70
0.15x = 0.70 - 0.25
0.15x = 0.45
x = 0.45/0.15
x = 3 dimes
Nickels = 8 nickels
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Sheila collect pokemon card. A of 2018, he ha a Mewtwo card that i twice a old a her Snorlax card. Two year ago, her rare Raichu card wa five time a old a the Snorlax card. If the Raichu card i even year older than the Mewtwo card in what year wa the Raichu card made?
The Raichu card was made 8 years ago.
To calculate this, we need to take into account the age of the Mewtwo card, the Snorlax card, and the Raichu card.
The Mewtwo card is twice as old as the Snorlax card, so the Mewtwo card is two years old. The Raichu card is five times as old as the Snorlax card, so it must be ten years old.
Since the Raichu card is two years older than the Mewtwo card, it must be eight years old. Therefore, the Raichu card was made eight years ago.
To summarise, the Mewtwo card is two years old, the Snorlax card is one year old, and the Raichu card is ten years old. Therefore, the Raichu card was made eight years ago.
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The area of a rectangle is 91 square inches. If the length of the rectangle is 1 less than twice its width, write an equation that could be used to find the width, w, of the rectangle.
The quadratic equation to find the width of the rectangle by formulating the area and length value is 2w² - w - 91 = 0.
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The value for the area of the rectangle is given as = 91 in²
Let the width for the rectangle be = w
Then the length of the rectangle is 1 less than twice its width, l = (2w - 1)
The formula for the area of the rectangle is -
Area = length × width
Substitute the values to get the equation for width -
91 = (2w - 1) × w
Use the arithmetic operation of multiplication -
91 = w(2w - 1)
91 = 2w² - w
Rearrange in quadratic form -
2w² - w - 91 = 0
Therefore, the equation is obtained as 2w² - w - 91 = 0.
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Emilio has a bank account that pays 4% interest each year. He has $200 in his account. How much interest will he earn after 1 year?
if you answer this right you will get extra brainly points
Answer:
Step-by-step explanation:
That"ll be 37% hope this helps:))
2. A manufacturer of flashlights wants to know how well one of their newer styles is selling in a chain of large home-improvement stores. They select a simple random sample of 20 stores, record how many of the flashlights were sold in a 30-day period, and construct a 95% confidence interval for the mean number of flashlights sold.
(a) If, instead of constructing a 95% confidence interval, the flashlight manufacturer constructed a 98% confidence interval, would the 98% interval be wider, narrower, or the same width as the 95% interval? Explain.
(b) How would the width of confidence interval change if the flashlight manufacturer took a larger sample? Explain.
(c) The 20 stores in the sample were actually the only stores who provided sales figures from 36 stores that were randomly chosen to be in the sample. Can the manufacturer adjust the confidence interval to take this nonresponse into account? If so, how? If not, why not?
A: (a) The 98% confidence interval would be wider than the 95% interval. As the confidence level increases, the margin of error increases, thus making the interval wider.
(b) The width of the confidence interval would decrease as the sample size increases. This is because a larger sample size will result in a more accurate representation of the population, thus allowing for a narrower confidence interval.
(c) The manufacturer cannot adjust the confidence interval to take this nonresponse into account, as the nonresponse does not affect the accuracy of the sample. The confidence interval is based on the sample itself and not the population from which it was drawn.
What is mean by random sample?Random sampling is a method of selecting a sample of individuals from a population such that each member of the population has an equal chance of being selected.
Random sampling is often used in research studies to ensure that the sample is representative of the population as a whole.
Random sampling is also used to minimize bias and ensure that the sample is not influenced by any particular group or individual.
Random sampling is important because it helps ensure that the results of the study are accurate and valid.
Random sampling helps to ensure that the sample is representative of the population and that the results are not influenced by any particular group or individual.
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Please help ASAP!!!!!!!!!
The slope of the line represented by 4x-7y=62 is 4/7. A line's steepness is measured by its slope. The mathematical expression for slope is "rise over run."
Option A is correct.
What is slope of line?In mathematics, a line's slope is the ratio of the change in the y coordinate to the change in the x coordinate. The net change in the y-coordinate and the net change in the x-coordinate, respectively, are denoted by the symbols delta y and delta x.
We are given equation as 4x-7y=62
First, let's write it in the slope-intercept form .In general, slope-intercept form is y=mx + b
where m is the slope
So, writing the equation in the form, we get
⇒-7y = 62-4x
⇒7y = 4x-62
⇒y = 4x/7-62/7
Now, matching the equation with the general form,
m = 4/7
Hence, the slope of the line represented by 4x-7y=62 is 4/7.
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Brett has c more comic books in his collection than Erica does. Erica has 19 comic books in her collection. Write an expression that shows how many comic books Brett has in his collection.
The expression for the given conditions is Y=10+c
where Y=no. of books Brett has and c=no. of books Erica has.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now
Given No. of books Erica has = 19
and Brett has c more comic books than Erica has
let Y=no. of books Brett has
Hence, the expression will be
Y=19+c
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Answer questions 8 and 9.
Find the measure of an arc from the central angle.
By using the property of measure of an arc from the central angle
m(arc MQN) = 225°
m(arc MPN) = 135°
If m(arc KJH) = 312°
m∠1 = 48°
What is the measure of an arc from the central angle?
The measure of an arc from the central angle is the portion of the circumference of a circle that the arc spans. The measure of an arc is typically given in degrees.
In the given figure
by using the property of measure of an arc from the central angle
m(arc MQN) = 225°
m(arc MPN) = 360° - 225° = 135°
In the second figure,
If m(arc KJH) = 312°
m∠1 = 360° - 312° = 48°
Hence, by using the property of measure of an arc from the central angle
m(arc MQN) = 225°
m(arc MPN) = 135°
If m(arc KJH) = 312°
m∠1 = 48°
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Need some help with this paper
well, it comes down to, if f(x) is indeed an inverse of g(x) and the other way around, then f( g(x) ) = x, and likewise g( f(x) ) = x, so let's check if f( g(x) =x
[tex]f(x)=3x+11\hspace{5em}g(x)=-\cfrac{1}{3}x-\cfrac{11}{3} \\\\[-0.35em] ~\dotfill\\\\ f(~~g(x)~~)=3\left( -\cfrac{1}{3}x-\cfrac{11}{3} \right)+11 \\\\\\ f(~~g(x)~~)=-x-11+11\implies f(~~g(x)~~)=-x ~~ \bigotimes[/tex]
now, we could do a test by doing g( f(x) ), however we don't need to, since f( g(x) ) ≠ x, they're not inverse of each other.
Zara has a rectangular garden. The length of her garden is 12 feet and the width is 7 feet.
She extends the width of her garden by w feet to create a larger garden with a total perimeter
of 46 feet. Write an equation that can be used to determine the amount of feet, w, by which
Zara extends the width of her garden.
By how many feet does Zara extend the width of her garden? Show your work.
Enter your equation, answer, and work in the space provided.
Zara extends the width of her garden by 11 feet. This can be calculated with the help of perimeter formula:
Equation used to solve the problem: P = 2L + 2W
2(12) + 2W = 46
24 + 2W = 46
2W = 22
W = 11
Zara extends the width of her garden by 11 feet.
The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.
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Which of the following numbers is irrational? (1 point)
a fraction with numerator negative 15 and denominator 4, a fraction with numerator negative 7 and denominator 9, square root of 4, π
The only number that is irrational is π
How to identify the number that is irrational?
An irrational number is a number that can't be written as the quotient between two integers.
Also, square roots of non-square numbers are irrational.
In this case, the options are:
-15/4
-7/9
√4
π
The first 3 of these are rational, and the only irrational one is π, which is the quotient betwen the cicumference and the diameter of a circle.
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6.4% as a fraction in simplest form
Answer:32/5
Step-by-step explanation:
32/5
Answer:
Solution: 6.4% as a fraction is 32/5.
Step-by-step explanation:
what sampling technique is being used in this scenario? voters are selected at random from an alphabetical list of all registered voters.
The sampling technique being used in this scenario is simple random sampling.
Simple Random Sampling TechniqueIt can be determined that simple random sampling is being used because individuals are selected at random from an alphabetical list of all registered voters. In simple random sampling, a random sample of individuals is selected from a larger population using a random procedure such as using a random number generator or drawing names out of a hat. The selection of individuals is completely random and every individual in the population has an equal chance of being selected.
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